https://file.aiquickdraw.com/mathbot/file/17247714613542zv5d66z.jpg

The graphs of the functions f(x) and g(x) are shown below. (a) Find (f · g)(1).

The image displays two functions, \( f(x) \) (in red) and \( g(x) \) (in blue), along with their corresponding graphs. The task is to find \( (f \cdot g)(1) \), which refers to the product of the function values of \( f(x) \) and \( g(x) \) at \( x = 1 \).

To solve \( (f \cdot g)(1) \):
1. Identify the values of \( f(1) \) and \( g(1) \) from the graph.
2. Multiply \( f(1) \) by \( g(1) \).

Let's break this down:

1. From the graph:
   - The value of \( f(1) \) (red curve) at \( x = 1 \) is approximately 3.
   - The value of \( g(1) \) (blue line) at \( x = 1 \) is approximately 2.

2. Now, compute \( (f \cdot g)(1) = f(1) \cdot g(1) \):
   \[
   (f \cdot g)(1) = 3 \cdot 2 = 6.
   \]

Thus, \( (f \cdot g)(1) = 6 \).

Would you like any further details or clarifications on this problem?

Here are 5 related questions you might find helpful:
1. How do you determine the values of a function from a graph at specific points?
2. What does the notation \( (f \cdot g)(x) \) represent in function operations?
3. Can the same procedure be used for any two functions \( f(x) \) and \( g(x) \)?
4. What is the significance of finding the product of two functions at a specific point?
5. How can you find the intersection points of two graphs algebraically?

**Tip:** When dealing with function graphs, it's essential to read values accurately from the axes, especially at key points like intersections and specified \( x \)-values.

Learn how to find (f · g)(1) by understanding function operations with detailed steps and graphical analysis. This problem involves evaluating the product of two functions at a specific point, illustrated with a graph. Suitable for high school students studying functions and graphs.

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